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多位数加法与进位：GeoGebra动态演示

多位数加法与进位：GeoGebra动态演示
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2023-06-01 20:47
几何作图
这个范例演示了如何使用GeoGebra工具进行多位数加法运算，并展示进位过程。核心数学概念包括进位规则和数位对齐。作图要点包括使用RandomUniform生成随机数、Take和Defined创建动态输入框、Join和Zip组合数位、If和Last处理进位逻辑。适合小学四年级至五年级学生，用于课堂练习和理解进位原理。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.9211549185010639, 0.1267217278194494, 0.4587814263304726, 0.5368644554618158, 0.3390788153979383, 0.9300646931809304, 0.398491521308098, 0.522113777373797, 0.3325706293470929, 0.36171803968431687, 0.6869834026922439, 0.10964751452049407, 0.6842278995733173, 0.7015568111129813, 0.09841935822458707, 0.6256479032317502, 0.029733057587366028, 0.0542107817156191, 0.43587920923227835, 0.6794076346993536, 0.028149962505182393, 0.8027416199359564, 0.14926409884188882, 0.4698585888255517, 0.17943233994717897, 0.2916390758699681, 0.5881070705440766, 0.2990208837113913, 0.06394590363415516, 0.7763085664508426, 0.214126780455786, 0.6706332204749167, 0.7706712333469542, 0.5570723601522938, 0.9225692445868733, 0.28916957715116565, 0.3948075766595067, 0.266243647841736, 0.3527794327757736, 0.13607784729833744, 0.8117374693696788, 0.2970574528535656, 0.6270279987041014, 0.15639423829374485, 0.32274015684082513, 0.10315413882487325, 0.632390531081673, 0.12989359846583395, 0.5884570948614829, 0.9369113985132874, 0.28343515288034926, 0.9066285166602697, 0.5989148715667421, 0.13420716242419484, 0.5036209716624476, 0.8070914814356606, 0.10390237682940998, 0.7521709179132233, 0.24064405698978697, 0.5623026820485046, 0.8546753201471978, 0.685142736745968, 0.4054888775525308, 0.3888811944695096, 0.9273276027019238, 0.0024092733446960126, 0.43665201685240246, 0.5886019340050679, 0.5597211140468485, 0.929322391129677, 0.3899019150727564, 0.4610702247512209, 0.11760611070573682, 0.3211318656529309, 0.050021880953453446, 0.601965239326686, 0.7114918053534779, 0.5562742569624781, 0.7042552890457812, 0.3378089170360624, 0.7739422133478701, 0.42296108663386794, 0.5576311345658399, 0.5614105466352005, 0.7372750191008859, 0.4896954536196591, 0.6079939717998193, 0.3100176440101695, 0.6541313118761543, 0.3368215146285965, 0.18339696972033562, 0.1907728503493742, 0.18806198589843545, 0.6323729624853155, 0.8565376952582422, 0.18533177066328244, 0.7381416803052139, 0.8813365891050432, 0.6401256851394597, 0.47744026712327087, 0.2006738815375708, 0.7829837136267132, 0.6834669440576469, 0.5639007135040909, 0.6222912390093673, 0.19614734312290677, 0.7841349214602985, 0.460674781476125, 0.9421825019508513, 0.22723473140103423, 0.15936856012877007, 0.6818766025194551, 0.34679308413640236, 0.2803644401125936, 0.5597972702639298, 0.5901030228374929, 0.40814877608278827, 0.6633047347907807, 0.24323930732397342, 0.7619288835871854, 0.7869426576552472, 0.10686416024881781, 0.24865340080909495, 0.42246348732213723, 0.19370229837251374, 0.5390475002930739, 0.019845881132404132, 0.22762039137187376, 0.9257206414627118, 0.6386397820036418, 0.08524351590253681, 0.4521957361081535, 0.34398562681803607, 0.8059185233045447, 0.763939748946931, 0.2159813853110337, 0.4730845414991431, 0.7909184804583108, 0.5993051849146789, 0.2989578288352215, 0.28798662421108323, 0.7620854407246247, 0.9797252542914372, 0.26011679105412, 0.7047224920925591, 0.26025557889061873, 0.33148644650988546, 0.5726578115634068, 0.3372821828281768, 0.5246834040434142, 0.47147958437873894, 0.05118323585065842, 0.600542961960361, 0.6393163858582837, 0.6872220594502563, 0.14408493499948563, 0.45871706010749846, 0.188676359833954, 0.06872271723649352, 0.6065713046519301, 0.46067341264332584, 0.4435570338588061, 0.22092194893976796, 0.5967271527626248, 0.20754101069962058, 0.8272850064788093, 0.7068361764296855, 0.40862942102056676, 0.6742417014421005, 0.7135148837096523, 0.4901197194916426, 0.18286019921657384, 0.9850275662418506, 0.8564425684526628, 0.8615286432323831, 0.1457647427321291, 0.3937134640327712, 0.48391969682307057, 0.32673009738388126, 0.44449453847758325, 0.1520984079799634, 0.3432390758540052, 0.49304721739697616, 0.23525767531704395, 0.12505890740406264, 0.2683365156991931, 0.1700635351135105, 0.39726602257866783, 0.43797608612501177, 0.34581537164444104, 0.10353251651901112, 0.30462520902510287, 0.6115226392247056, 0.2755508721018255, 0.7337464352303676, 0.9428563217411082, 0.9103891712144115, 0.45966745315187496, 0.5884160584703197, 0.1558697045891217}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Take({input11, input12, input13, input14, input15, input16}, 1, randomNum1) → inputBelow
  4. Defined(IndexOf[true, Zip[nn ≥ 10, nn, inputBelow]]) → showWarning
  5. Take({input1, input2, input3, input4, input5}, 1, randomNum1 - 1) → inputAbove
  6. Join({inputAbove, inputBelow}) → inputCurrent
  7. Zip(If[nn ≤ 0.5, 1, 0], nn, Take[currentRandomSeeds, 2, 7]) → carryOrNot
  8. If(¬Defined[IndexOf[1, Last[carryOrNot, randomNum1 - 1]]], {0, 0, 0, 0, 1, 0}, carryOrNot) → carryOrNot2
  9. Last(Zip[If[nn ≟ 1, Max[1, pp], pp], nn, carryOrNot2, pp, num1], randomNum1) → num1_2
  10. Zip(If[nn ≟ 0, Min[9 - pp, qq], Max[10 - pp, qq]], nn, Last[carryOrNot2, randomNum1], pp, num1_2, qq, num2) → num2_2
  11. If(num1_2(1) + num2_2(1) ≥ 8 ∨ num2_2(1) ≟ 0, Join[{{Max[floor(num2_2(1) / 2), 1]}, Last[num2_2, randomNum1 - 1]}], num2_2) → num2_{3}
  12. Zip(If[¬Defined[nn], 0, nn], nn, inputAbove) → inputAboveToCompare
  13. If(num1_2(1) + num2_2(1) ≥ 8 ∨ num1_2(1) ≟ 0, Join[{{Max[floor(num1_2(1) / 2), 1]}, Last[num1_2, randomNum1 - 1]}], num1_2) → num1_{3}
  14. If(num1_{3}(-1) + num2_{3}(-1) + c1 ≥ 10, 1, 0) → c2
  15. If(num1_{3}(-2) + num2_{3}(-2) + c2 ≥ 10, 1, 0) → c3
  16. If(num1_{3}(-3) + num2_{3}(-3) + c3 ≥ 10, 1, 0) → c4
  17. If(num1_{3}(-4) + num2_{3}(-4) + c4 ≥ 10, 1, 0) → c5
  18. If(num1_{3}(-5) + num2_{3}(-5) + c5 ≥ 10, 1, 0) → c6
  19. Last({c6, c5, c4, c3, c2, c1}, randomNum1) → carryOrNotSol
  20. Zip(If[nn ≟ 0, 0, nn + mm], nn, carryOrNotSol, mm, num1_{3}) → carrySecondMethod
  21. Zip(Mod[nn, 10], nn, result) → result2
  22. Reverse(Sequence[{carrySecondMethod(ii), result2(ii)}, ii, 1, Length[result2]]) → InputExpected2
  23. Reverse(Sequence[{carryOrNotSol(ii), result2(ii)}, ii, 1, Length[result2]]) → InputExpected1
  24. Reverse(Sequence[{Element[Append[inputAboveToCompare, 0], ii], inputBelow(ii)}, ii, 1, Length[result2]]) → InputPairs
  25. Zip(AreEqual[L1, L2], L1, InputPairs, L2, If[secondMethod, InputExpected2, InputExpected1]) → ForHint
  26. Zip(If[nn ≟ 0, 0, 1], nn, ForHint) → ForHint2
  27. Zip(If[nn ≟ 0, "", "1"], nn, carryOrNotSol) → carryOrNotText
  28. Append("", Zip[(If[secondMethod ∧ mm ≠ 0, "\cancel", ""] * Text[nn]), nn, num1_{3}, mm, Append[inputAboveToCompare, 0]]) → num1_3Text
  29. Append("+", Zip[Text[nn], nn, num2_{3}, mm, Reverse[Sequence[randomNum1]]]) → num2_3Text
  30. Zip(If[nn ≟ 1, (("\cancel{" * mm) * "}"), Text[mm]], nn, carryOrNotSol, mm, num1_{3}) → num1WithCancel
  31. Append("", Zip[If[nn ≟ 0, "", Text[nn]], nn, carrySecondMethod]) → carrySecondMethodText
  32. Textfield(input1) → InputBox1
  33. Textfield(input2) → InputBox2
  34. Corner(5) → layoutAppSize
  35. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  36. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  37. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  38. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  39. Textfield(input3) → InputBox3
  40. Textfield(input4) → InputBox4
  41. Textfield(input5) → InputBox5
  42. Textfield(input11) → InputBox11
  43. Textfield(input12) → InputBox12
  44. Textfield(input13) → InputBox13
  45. Textfield(input15) → InputBox15
  46. Textfield(input16) → InputBox16
  47. Sequence(87 + (ii * 45), ii, 0, 6) → xPosIB, {87, 132, 177, 222, 267, 312, 357}
  48. Translate(vGL, Vector[(Vector[Corner[1], Corner[2]] / 800 * 8)]) → vGL'
  49. Textfield(input14) → InputBox14
  50. TableText(Append["", carryOrNotText], num1_3Text, num2_3Text, Append["", result2], "c_00010") → solTableM1
  51. TableText(carrySecondMethodText, Append["", num1WithCancel], num2_3Text, Append["", result2], "c_00010") → solTableM2
  52. TableText(num1_3Text, num2_3Text, "c_001", 45, 30) → text1
  53. Sequence(80 + (ii * 45), ii, 0, 6) → xPosIBBelow, {80, 125, 170, 215, 260, 305, 350}
  54. Flatten({Sequence["white", ii, 1, indexHintL - 1], If[¬correct, {If[enableInput, orangeIB, redIB]}, {}], Sequence[tealIB, ii, 1, randomNum1]}) → colorIBHint
  55. Flatten({Sequence["white", ii, 1, indexHintL - 1], If[(¬correct) ∧ carryError, {If[enableInput, orangeIB, redIB]}, {}], Sequence[tealIB, ii, 1, randomNum1]}) → colorIBupHint
  56. Zip(If[nn ≟ mm, tealIB, redIB], nn, result2, mm, inputBelow) → colorIBSol
  57. If(enableInput, colorIBHint, colorIBSol) → colorIB
  58. Zip(If[nn ≟ mm, tealIB, redIB], nn, inputAboveToCompare, mm, If[secondMethod, carrySecondMethod, carryOrNotSol]) → colorIBupSol
  59. If(enableInput, colorIBupHint, colorIBupSol) → colorIBup
  60. Zip(If[ii ≟ jj ∧ ii ≠ kk, 2, ii ≟ kk ∧ ii ≠ jj, 1, 0], ii, inputAboveToCompare, jj, carrySecondMethod, kk, carryOrNotSol) → l1

AI 绘图提示语参考

绘制一个多位数加法竖式练习图，包含两个随机生成的多位数（上方和下方），数字按位对齐，并显示进位标记。图中包含多个输入框用于填写数字，以及提示区域显示进位过程。图形布局为竖式加法格式，上方数字和下方数字分别排列，进位数字以小型标记显示在相应列上方，结果区域预留空白。整体设计用于教学演示，突出进位和数位对齐的概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。